Some responses here indicate that not everyone understood the OP. There's a massive difference between a pop system like what's used in Victoria, Stellaris and Imperator and a population count. Obviously one may disagree with the latter anyway, but my point here is that you should know what you're disagreeing with.
Pops are a resource hog, because you need to calculate a whole plethora of stats for each individual pop. Depending on the game it's things like happiness, faction, race, ethnicity, religion, employment and promotion opportunities. So on and so forth. For each pop. You also can (and in many cases are encouraged to) actively interact with some of the pops, where you manually change their employment, religion and so on. Which creates a lot of micromanagement. And even when you reduce the micromanagement you may end with a system that's just more obscure (I tried both release Imperator and the recent 2.0 version that reduced micromanagement and I was actually more confused in the 2.0 version because I had absolutely no clue about why I should care about the pops at all after most of the direct interactions with them have been removed).
Meanwhile a population counter is just a number, which makes it a much simpler system. You may want it to do more than one thing (like in CK3 it could affect revenue and the amount of levies in a province), but it's essentially just a multiplier for that calculation, just like some buildings are. There's also much less (if at all) direct interaction here like you have with pops and instead you'd be affecting that indirectly by doing things you already do, like building buildings, researching certain innovations, maybe passing certain laws.
While there is indeed a subset of PDS games's fans that swears by pops as the magical panaceum to all of Paradox's games' problems that would make each Paradox game instantly better, I wholeheartedly disagree with that assertion. I think when it comes to Crusader Kings in particular pops would utterly suck. First of all, given the time period stark majority of your pops would be peasants. Which would not make for a very interesting mechanic in my opinion. You could double down on the peasants and reflect the historical fact of how there were different types of them, with some of them being rather rich, but I think that would create too much focus on peasantry in a game mostly about rulers. Secondly, given the limited social mobility in this time period, it would defeat one of the main purposes of the pop system, i.e. a diversified economy with various jobs that the pops can shift between, potentially advancing on the social ladder in the process (like how Stellaris pops can go from workers to specialists and then rulers).
Thirdly, there's the issue of game performance. Stellaris already struggles with it. 3.0 tried to address it by slowing down your pop growth in the late game, creating a rather unsatisfying framework where many of your planets are just empty (instead of just halving the amount of pops you need and doubling the productivity of each job). But I digress. The thing to keep in mind here is the amount of planets that have pops on them. Even on the largest galaxy map that has a 1000 star systems, the majority of systems has no colonizable planets. And when it comes to systems that have such planets, most of them have just one. Eventually you can unlock the ability to construct artificial habitats (and, later on, ringworlds) that can also be colonized, but that's heavily limited by resources. As such, even in a game that uses the large 1000 star system maps, with a standard amount of habitable worlds you may have somewhere between 100-200 colonized planets among all empires by the late game. And the game still slows down despite the aforementioned 3.0 changes.
Then look at CK3. It'd make little sense to have pops be duchy-level or higher. Since they'd most likely work with buildings in some way, they should be based on counties, if not baronies. The thing is, CK3 has more than 2500 counties. My current Stellaris game where I used the setting to have double the standard amount of colonizable planets has slightly above 250 colonized planets among all empires in the late game. That's tenfold increase. And CK3 already has thousands of individual characters with their goals and personalities to calculate on top of that. A pop system in CK3 would be a performance nightmare.
Now let's loop back to population number. A good point of reference here are Total War games. Not all of them, as Warhammer for example has a much simplified campaign in this department (though various races have their own special campaign mechanics to compensate), but games like Medieval II or the recent Three Kingdoms have population numbers as a mechanic. And while Total War can be intensive performance-wise during battles, the campaign is pretty much smooth sailing. Even though, like I said, it can do more than one thing. In Three Kingdoms for example it affects income, replenishment, public order and building speed. And the population itself has its own growth statistic, affected by reforms, public order and infrastructure.
Like I said, I wholeheartedly disagree with a pop system in CK3. But the same does not apply to a population count. I think a population count would fit right in in this game. Someone mentioned development, but that's not really the same thing. Thematic-wise development represents the quality of the land, be it in available arable area for the peasants or the quality of infrastructure. Meanwhile population count represents the quantity of the people working that land. They are two complementary parts of the whole picture.
And to address another concern expressed in this thread about how this doesn't fit the main scope of the game, population should very much be something of concern to a medieval ruler. It was one of the main resources of a medieval society. And one of the main reasons why upper classes of society forced rulers to pass privileges that limited lower classes, particularly the mobility of the peasants. It was to ensure they had enough people working their own fields, instead of them moving to better pastures.
Anyway, moving on to the way I envision it in CK3. It'd be mostly based on Total War, specifically Medieval II and Three Kingdoms I already mentioned. Like I said early on, I think population count in CK3 should first and foremost act as a modifier to your levies and income. Then there's growth of the population. There could be multiple things affecting it, like buildings or certain innovations. I think prosperity system from CK2 could also make a return. That way you'd have an extra incentive to protect your own holdings from raiders or from foreign armies during wars. In case of the latter in particular you could be forced to choose between besiegeing enemy territory or protecting your own. That way you'd have another layer of interaction with your own holdings, which currently is pretty much limited to simply building buildings. Another returning thing from CK2 would be the epidemic mechanic, particularly the ability to build hospitals to protect your holdings from them.
There's also the subject of religion and culture. I think Medieval II did this one (well, it did religion, I don't recall it having culture, but it should work fine for both regardless) in a manner that'd be appropriate for Crusader Kings. It simply represented each religion as a percentage of the total. So it wouldn't be a resource hog like a pop system where you'd have pop named John that's unhappy because he's a Catholic and the ruler oppresses them and then you'd have a second pop named Reginald that's also unhappy because he's a Catholic, needing his own separate calculations. Instead you'd have a population of say, 10k and 5% are Catholic, with corresponding penalties to province stability based on religious unrest. That way when the population grows the game wouldn't need to make additional calculations like "which religion the new pops are going to have?", that number will just stay at 5% until you actually do something about it, like send in your realm priest to convert them.
Speaking of which, the way CK3 currently works make each county mono-cultural and mono-religious, which is just unrealistic and not immersive at all. Representing minorities would introduce granularity and depth here. It'd also make potential rebellions represent the disgruntled population better. And when you'd send your council members to convert the culture or religion, it'd simply shift the percentages around, allowing you to see the progress in a more understandable way.
And while I'm on this topic, I want to address something. While I personally did not like the sheer RNG of conversion in CK2, I think CK3 went too far in the other direction with its "guaranteed conversion in X years". And the thing is, CK3 itself already has a much better system, i.e. the progress bar of schemes. There are multiple reasons why I think it is superior to both CK2's and CK3's conversion. First of all, it's never 100% guaranteed. On the other hand, it does not force you to resign to simply playing to RNGesus. Your chance to progress each month is based on clearly available stats. Finally, it has various events that may affect your progress or the end success chance in various ways, particularly with options that may have trade-offs or options that vary in potential depending on your other stats.
Anyway, back to population. Like I said, Medieval II only had religion, while CK3 also has culture. So let's use Halfdan as example. You start conquering England and have Norsemen and Anglo-Saxons in your realm, as well as followers of Asatru and Catholicism. Should that mean you'd have a separate counter for Asatru Norse, Asatru Anglo-Saxons, Catholic Norse and Catholic Anglo-Saxons?
I don't think so. I think having two simple and separate religion and culture categories based on the Medieval II system where you have X% Norse and Y% Anglo-Saxon on one track while having A% Asatru and B% Catholic on the other is enough. That way you'd stay with just two counters no matter how many minorities you have in a given province. It's a simplification, sure, but one I think is necessary for the impact it'd have on performance. That way you'd also keep populist and religious uprisings thematically separate. After all, if people are rebelling because their Catholic religion is persecuted then it won't matter to them whether they are Norse or Anglo-Saxons, they are persecuted regardless. The same applies to situations where they feel persecuted due to their religion and form a religious rebel faction.
And while I'm on the topic of rebellions, you should be able to influence the likelihood of that happening in ways other than simply eliminating the problematic cultures through conversion. The culture in particular is rather annoying, because the game motivates you to convert them, otherwise you keep getting swarmed by populist revolts. Meanwhile the medieval period was rather multi-cultural and many cultures coexisted in the same realm. But don't worry, I don't mean anything like micromanaging pops. Just the opposite, I'm talking about macromanagement. What I have in mind is a tab similar to factions that shows all the minorities present in your realm that you can do stuff with.
Think accepted cultures in EU4. Or culture decisions in Imperator. While Imperator does have micromanagement of pops, it also has culture-wide decisions, like forming a honor guard from a specific integrated (or, using the aforementioned UE4 terminology, accepted) culture or giving certain rights to cultures (that vary between integrated and non-integrated cultures). Obviously these should not be copy-pasted from Imperator since it's a different time period with different culture dynamics, but there's a plethora of potential options you could have. The honor guard is actually something you could copy from Imperator, because that's what the Byzantines did with the Varangian guard. You could also raise special taxes or making certain groups exempt from religious tax if you have such a tenet. You could forcibly conscript children of specific groups into military slavery and have your own mamluks and jannisaries. You could expel certain minorities and confiscate their goods. So on and so forth.
Then there's the subject of minorities appearing in provinces. Lowering their number is simple, you can achieve that by conversion or the above example of expulsion. But how would new minorities appear to represent a more open society (if that's what you're going for with the cultural decisions, obviously)? A migration between provinces is a no-go in my opinion. Whether it's pops or population number, it's going to be a resource hog, starting with checking things like province adjacency. So once again I'd go with a more abstract and simplified solution. If you have a certain minority within your entire realm and you give them certain rights, like commerce rights, settlement rights or the right of movement to peasants, you'd have a chance for a minority to appear as a percentage in your other holdings, without disappearing elsewhere. Like I said, it's an abstraction, but I don't think it'd a bad thing here.
Another thing that could affect it are actual characters. You have a knight from another culture? Then that culture could appear as a minority in your holdings. After all, knights still had their own manors where they would settle with their families, even if they are not a landed character as the game understands it. Or perhaps you have a wife from a different culture. In this case you could even have events about how she's home-sick and asks you to hire servants from her culture, creating an influx of characters of said culture. Characters could also affect the religion in a more direct way. Perhaps your courtiers convert to some heresy and, in neophyte zeal, start spreading their new gospel. Which is also a venue for some events that would let you handle such situations.
Finally, there's a difference in regards to population between Medieval II and Three Kingdoms Total War games that I want to address. I.e. how the numbers in Medieval are much lower, generally in tens of thousands, in some places growing to hundreds of thousands later in the game. Meanwhile Three Kingdoms has a load of settlements with the population in the millions because China. The Medieval II's numbers are much more apt for non-Chinese parts of Medieval world in general. Most cities of that time period were precisely in that tens of thousands to perhaps hundreds of thousands.
But there were some exceptions, like Paris, Baghdad or Constantinople. Which is why I think CK3 could incorporate something like the Cities of Wonders 2 mod that adds a new metropolis holding type into the game, because having Constantinople be represented as a castle is rather weird. Admittedly, people did tend to migrate to such cities even in the medieval period, but I think there's a solution to that that doesn't require the aforementioned actual migration with adjacency checking, calculations and whatnot. And it revolves around duchies. If you have a metropolis in a given duchy, all other holdings in it would simply get a hefty penalty to their own population growth, while the metropolis would get a large increase. Another abstract simplification, but it's another case where I think it's apt from both the perspective of mechanics and performance, as well as the main themes of CK3.
